1
GATE ME 2017 Set 1
+2
-0.6
$$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$ and $$\,\,R\,\,\,\left( {1,5} \right)\,\,\,$$ are three points on the curve defined by $$\,\,f\left( x \right),\,\,$$ Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $$x=0$$ and $$x=1$$ for the curve. The difference between the two results will be
A
$$0$$
B
$$0.25$$
C
$$0.5$$
D
$$1$$
2
GATE ME 2016 Set 2
Numerical
+2
-0
The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,}$$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi$$ is _________.
3
GATE ME 2016 Set 1
Numerical
+2
-0
Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.
4
GATE ME 2016 Set 1
Numerical
+2
-0
Gauss-Seidel method is used to solve the following equations (as per the given order). $${x_1} + 2{x_2} + 3{x_3} = 5$$$$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$\,3{x_1} + 2{x_2} + {x_3} = 3$$\$
Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.